β Scribed by Dr. Tosio Kato (auth.)
No coin nor oath required. For personal study only.
In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition. Little change has been made in the text except that the paraΒ graphs V-Β§ 4.5, VI-Β§ 4.3, and VIII-Β§ 1.4 have been completely rewritten, and a number of minor errors, mostly typographical, have been corrected. The author would like to thank many readers who brought the errors to his attention. Due to these changes, some theorems, lemmas, and formulas of the first edition are missing from the new edition while new ones are added. The new ones have numbers different from those attached to the old ones which they may have replaced. Despite considerable expansion, the bibliography i" not intended to be complete. Berkeley, April 1976 TosIO RATO Preface to the First Edition This book is intended to give a systematic presentation of perturbaΒ tion theory for linear operators. It is hoped that the book will be useful to students as well as to mature scientists, both in mathematics and in the physical sciences.
Front Matter....Pages I-XXI
Operator theory in finite-dimensional vector spaces....Pages 1-62
Perturbation theory in a finite-dimensional space....Pages 62-126
Introduction to the theory of operators in Banach spaces....Pages 126-188
Stability theorems....Pages 189-250
Operators in Hilbert spaces....Pages 251-308
Sesquilinear forms in Hilbert spaces and associated operators....Pages 308-364
Analytic perturbation theory....Pages 364-426
Asymptotic perturbation theory....Pages 426-479
Perturbation theory for semigroups of operators....Pages 479-515
Perturbation of continuous spectra and unitary equivalence....Pages 516-567
Back Matter....Pages 568-622
Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization
π SIMILAR VOLUMES
This text, part of the "Springer Classics of Mathematics" series, examines perturbation theory for linear operators.
From the reviews: "[β¦] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory. [β¦] I can recommend
<p>This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions